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POST UTME UNILORIN 2018 Mathematics | Objective

Are you preparing for POST UTME UNILORIN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the area under the curve $ y = \frac{1}{2}x^2 + 3x - 2 $ from $ x = 0 $ to $ x = 4 $.

A. ( 4 )

B. ( 8 )

Correct C. ( 12 )

D. ( 16 )

Correct Answer: C

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Question 2

Solve the inequality $ 2x^2 + 5x - 3 > 0 $ u\sing the quadratic formula.

Correct A. $ x < -1 $ or $ x > 3 $

B. $ x < -3 $ or $ x > 1 $

C. $ x < 1 $ or $ x > 3 $

D. $ x < -3 $ or $ x > -1 $

Correct Answer: A

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Question 3

A bag contains 5 red marbles, 8 blue marbles, and 12 green marbles. If a marble is drawn at random, what is the probability that it is not blue?

A. $ \frac{1}{3} $

B. $ \frac{2}{5} $

C. $ \frac{3}{5} $

Correct D. $ \frac{4}{5} $

Correct Answer: D

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Question 4

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the power rule.

Correct A. ( f'(x) = 6x + 2 )

B. ( f'(x) = 3x^2 + 2x - 5 )

C. ( f'(x) = 6x - 2 )

D. ( f'(x) = 3x^2 - 2x + 5 )

Correct Answer: A

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Question 5

A circuit consists of a 12V battery, a 4Ω resistor, and a 6Ω resistor connected in series. What is the total resis\tance of the circuit?

A. ( 8Ω )

B. ( 10Ω )

Correct C. ( 12Ω )

D. ( 16Ω )

Correct Answer: C

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Question 6

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 7

Solve the quadratic equation $ x^2 + 5x + 6 = 0 $ u\sing the quadratic formula.

Correct A. -2

B. -3

C. -1

D. 1

Correct Answer: A

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Question 8

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is its volume?

Correct A. 72

B. 80

C. 90

D. 100

Correct Answer: A

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Question 9

A circle has a radius of 4 cm. What is its circumference?

Correct A. 8π

B. 10π

C. 12π

D. 16π

Correct Answer: A

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Question 10

A matrix A has the following elements: $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} $. What is the determinant of matrix A?

A. -2

Correct B. 0

C. 2

D. 4

Correct Answer: B

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Question 11

Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = egin{cases} 2x, & 0 < x < 1 \ 0, & \text{otherwise} \end{cases}$ and $f_Y(y) = egin{cases} 3y^2, & 0 < y < 1 \ 0, & \text{otherwise} \end{cases}$. Find the probability that $X + Y < 1$.

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 12

Solve for $x$: $\log_{10}$ x^2 $ = 4$.

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 13

Find the volume of the solid formed by revolving the region bounded by $y = x^2$, $y = 0$, and $x = 2$ about the $x$-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 14

In the diagram below, $ABCD$ is a square with side length $s$. If $E$ is the midpoint of $AD$, find the length of $BE$.

A. \frac{s}{2}

B. s

Correct C. \frac{\sqrt{2}s}{2}

D. s\sqrt{2}

Correct Answer: C

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Question 15

Find the area of the region bounded by $y = x^2$, $y = 0$, and $x = 2$.

A. 8

Correct B. 16

C. 32

D. 64

Correct Answer: B

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Question 16

Let X and Y be indep\endent random variables with probability density functions f_X(x) = \\begin{cases} 2x, & 0 < x < 1 \\ 0, & \text{otherwise} \\end{cases} and f_Y(y) = \\begin{cases} 3y^2, & 0 < y < 1 \\ 0, & \text{otherwise} \\end{cases}. Find P$ X > Y $.

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 17

Find the derivative of the function f(x) = \frac{1}{x^2 + 1} u\sing the chain rule.

A. -\frac{2x}{$ x^2 + 1 $^2}

Correct B. \frac{2x}{$ x^2 + 1 $^2}

C. -\frac{2}{$ x^2 + 1 $^2}

D. \frac{2}{$ x^2 + 1 $^2}

Correct Answer: B

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Question 18

Solve the inequality \log_2$ x^2 - 4 $ > 2.

Correct A. x < -2 or x > 2

B. x < 2 or x > 4

C. x < -4 or x > 4

D. x < -2 or x > 4

Correct Answer: A

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Question 19

Find the area under the curve y = x^2 from x = 0 to x = 2.

Correct A. \frac{8}{3}

B. \frac{16}{3}

C. \frac{32}{3}

D. \frac{64}{3}

Correct Answer: A

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Question 20

A polynomial function f(x) has zeros at x = -2, x = 1, and x = 3. If f$ -1 $ = 16, find f(2).

A. -16

B. 16

C. 32

Correct D. 64

Correct Answer: D

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Question 21

Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = 2x$ for $0 < x < 1$ and $f_Y(y) = 3y^2$ for $0 < y < 1$. Find the probability that $X + Y < 1$.

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 22

Find the equation of the circle with center $$ -2, 3 $$ and radius $4$.

Correct A. $ x + 2 $^2 + $ y - 3 $^2 = 16

B. $ x - 2 $^2 + $ y + 3 $^2 = 16

C. $ x + 2 $^2 + $ y + 3 $^2 = 16

D. $ x - 2 $^2 + $ y - 3 $^2 = 16

Correct Answer: A

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Question 23

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

Correct A. 0.8413

B. 0.8413

C. 0.8413

D. 0.8413

Correct Answer: A

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Question 24

Solve the inequality $x^2 + 4x + 4 > 0$.

Correct A. $ -\infty, -2 $ \cup $ 2, \infty $

B. $ -\infty, 2 $ \cup $ 2, \infty $

C. $ -\infty, -2 $ \cup $ -2, 2 $ \cup $ 2, \infty $

D. $ -\infty, -2 $ \cup $ 2, \infty $

Correct Answer: A

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Question 25

Find the area under the curve $y = x^2$ from $x = 0$ to $x = 2$.

Correct A. \frac{8}{3}

B. \frac{4}{3}

C. \frac{2}{3}

D. \frac{1}{3}

Correct Answer: A

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